Lesson 1
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 1: Positive and Negative Numbers on the Number Line—
Opposite Direction and Value
Exit Ticket
1.
If zero lies between 𝑎𝑎 and 𝑑𝑑, give one set of possible values for 𝑎𝑎, 𝑏𝑏, 𝑐𝑐, and 𝑑𝑑.
𝑎𝑎
2.
𝑏𝑏
𝑑𝑑
Below is a list of numbers in order from least to greatest. Use what you know about the number line to complete
the list of numbers by filling in the blanks with the missing integers.
−6, −5,
3.
𝑐𝑐
, −3, −2, −1,
, 1, 2,
, 4,
,6
Complete the number line scale. Explain and show how to find 2 and the opposite of 2 on a number line.
0
Lesson 1:
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2
Positive and Negative Numbers on the Number Line—Opposite Direction
and Value
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Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 2: Real-World Positive and Negative Numbers and Zero
Exit Ticket
1.
Write a story problem that includes both integers −8 and 12.
2.
What does zero represent in your story problem?
3.
Choose an appropriate scale to graph both integers on the vertical number line. Label the scale.
4.
Graph both points on the vertical number line.
Lesson 2:
© 2015 Great Minds. eureka-math.org
G6-M3-SAP-1.3.0-07.2015
Real-World Positive and Negative Numbers and Zero
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2
Lesson 3
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 3: Real-World Positive and Negative Numbers and Zero
Exit Ticket
1.
Write a story problem using sea level that includes both integers −110 and 120.
2.
What does zero represent in your story problem?
3.
Choose an appropriate scale to graph both integers on the vertical number line.
4.
Graph and label both points on the vertical number line.
Lesson 3:
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Real-World Positive and Negative Numbers and Zero
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3
Lesson 3
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Exploratory Challenge Station Record Sheet
#𝟏𝟏
Poster # _______
#𝟐𝟐
#𝟑𝟑
#𝟒𝟒
#𝟓𝟓
Integers: ___________________
Number Line Scale: ________
Poster # _______
Integers: ___________________
Number Line Scale: ________
Poster # _______
Integers: ___________________
Number Line Scale: ________
Poster # _______
Integers: ___________________
Number Line Scale: ________
Poster # _______
Integers: ___________________
Number Line Scale: ________
Lesson 3:
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G6-M3-SAP-1.3.0-07.2015
Real-World Positive and Negative Numbers and Zero
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4
Lesson 4
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 4: The Opposite of a Number
Exit Ticket
In a recent survey, a magazine reported that the preferred room temperature in the summer is 68°F. A
wall thermostat, like the ones shown below, tells a room’s temperature in degrees Fahrenheit.
Sarah’s Upstairs Bedroom
Downstairs Bedroom
72℉
64℉
a.
Which bedroom is warmer than the recommended room temperature?
b.
Which bedroom is cooler than the recommended room temperature?
c.
Sarah notices that her room’s temperature is 4°F above the recommended temperature, and
the downstairs bedroom’s temperature is 4°F below the recommended temperature. She
graphs 72 and 64 on a vertical number line and determines they are opposites. Is Sarah
correct? Explain.
d.
After determining the relationship between the temperatures, Sarah now decides to represent
72°F as 4 and 64°F as −4 and graphs them on a vertical number line. Graph 4 and −4 on the
vertical number line on the right. Explain what zero represents in this situation.
Lesson 4:
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0
The Opposite of a Number
5
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Lesson 5
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 5: The Opposite of a Number’s Opposite
Exit Ticket
1.
Jane completes several example problems that ask her to the find the opposite of the opposite of a number, and for
each example, the result is a positive number. Jane concludes that when she takes the opposite of the opposite of
any number, the result will always be positive. Is Jane correct? Why or why not?
2.
To support your answer from the previous question, create an example, written as an equation. Illustrate your
example on the number line below.
Lesson 5:
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G6-M3-SAP-1.3.0-07.2015
The Opposite of a Number’s Opposite
6
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Lesson 6
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 6: Rational Numbers on the Number Line
Exit Ticket
Use the number line diagram below to answer the following questions.
𝐾𝐾
0
−1
1
1.
What is the length of each segment on the number line?
2.
What number does point 𝐾𝐾 represent?
3.
What is the opposite of point 𝐾𝐾?
4.
Locate the opposite of point 𝐾𝐾 on the number line, and label it point 𝐿𝐿.
5.
In the diagram above, zero represents the location of Martin Luther King Middle School. Point 𝐾𝐾 represents the
library, which is located to the east of the middle school. In words, create a real-world situation that could
represent point 𝐿𝐿, and describe its location in relation to 0 and point 𝐾𝐾.
Lesson 6:
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Rational Numbers on the Number Line
7
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Lesson 7
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 7: Ordering Integers and Other Rational Numbers
Exit Ticket
In math class, Christina and Brett are debating the relationship between two rational numbers. Read their claims below,
and then write an explanation of who is correct. Use a number line model to support your answer.
1
2
1
2
Christina’s Claim: “I know that 3 is greater than 2 . So, −3 must be greater than −2 .”
1
2
Brett’s Claim: “Yes, 3 is greater than 2 , but when you look at their opposites, their order will be opposite. So, that
1
2
means −2 is greater than −3.”
Lesson 7:
© 2015 Great Minds. eureka-math.org
G6-M3-SAP-1.3.0-07.2015
Ordering Integers and Other Rational Numbers
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Lesson 8
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 8: Ordering Integers and Other Rational Numbers
Exit Ticket
Order the following set of rational numbers from least to greatest, and explain how you determined the order.
1
2
1
3
−3, 0, − , 1, −3 , 6, 5, −1,
Lesson 8:
© 2015 Great Minds. eureka-math.org
G6-M3-SAP-1.3.0-07.2015
21
5
,4
Ordering Integers and Other Rational Numbers
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9
Lesson 9
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 9: Comparing Integers and Other Rational Numbers
Exit Ticket
1.
Interpret the number line diagram shown below, and write a statement about the temperature for Tuesday
compared to Monday at 11:00 p.m.
50
Monday’s Temperature (°F) at 11:00 p.m.
0
Tuesday’s Temperature (°F) at 11:00 p.m.
−50
2.
If the temperature at 11:00 p.m. on Wednesday is warmer than Tuesday’s temperature but still below zero, what is
a possible value for the temperature at 11:00 p.m. Wednesday?
Lesson 9:
© 2015 Great Minds. eureka-math.org
G6-M3-SAP-1.3.0-07.2015
Comparing Integers and Other Rational Numbers
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10
6•3
Lesson 9
NYS COMMON CORE MATHEMATICS CURRICULUM
Activity Cards—Page 1
The Navy Seals are practicing
new techniques. The blue
submarine is 450 ft. below
sea level, while the red
submarine is 375 ft. below
sea level.
Colorado is known for drastic
changes in temperatures.
Tuesday morning the
temperature was 32°F, but
Tuesday night the
temperature was
−3°F.
Holly sold lemonade two days
in a row. On Saturday, Holly
earned $5.75. On Sunday,
Holly earned $3.25.
−𝟓𝟓𝟓𝟓𝟓𝟓 −𝟒𝟒𝟒𝟒𝟒𝟒 −𝟑𝟑𝟑𝟑𝟑𝟑 −𝟐𝟐𝟐𝟐𝟐𝟐 −𝟏𝟏𝟏𝟏𝟏𝟏
−𝟒𝟒
−𝟐𝟐 −𝟏𝟏
Lesson 9:
© 2015 Great Minds. eureka-math.org
G6-M3-SAP-1.3.0-07.2015
𝟎𝟎
𝟒𝟒
𝟖𝟖
𝟎𝟎
𝟏𝟏𝟏𝟏 𝟏𝟏𝟏𝟏 𝟐𝟐𝟐𝟐 𝟐𝟐𝟐𝟐 𝟐𝟐𝟐𝟐 𝟑𝟑𝟑𝟑
𝟎𝟎 𝟏𝟏 𝟐𝟐 𝟑𝟑 𝟒𝟒 𝟓𝟓 𝟔𝟔 𝟕𝟕 𝟖𝟖
Dolphins love to jump out of
the water. Dolly, the dolphin,
can jump 5 meters above the
water and swim 450 meters
below the surface of the
water.
The high school football team
lost 8 yards on first down.
On second down, the team
gained 2 yards.
In golf, the lowest score wins.
Pete’s final score was −2,
and Andre’s final score was
−5.
−𝟒𝟒𝟒𝟒𝟒𝟒 −𝟑𝟑𝟑𝟑𝟑𝟑 −𝟐𝟐𝟐𝟐𝟐𝟐 −𝟏𝟏𝟏𝟏𝟏𝟏
−𝟖𝟖
−𝟕𝟕
−𝟔𝟔
−𝟒𝟒
−𝟐𝟐
−𝟓𝟓
−𝟑𝟑
−𝟏𝟏
𝟎𝟎
𝟎𝟎
𝟎𝟎
𝟐𝟐
𝟏𝟏
𝟑𝟑
Comparing Integers and Other Rational Numbers
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11
Lesson 9
NYS COMMON CORE MATHEMATICS CURRICULUM
6•3
Activity Cards—Page 2
Teagon earned $450 last
month cutting grass. Xavier
spent $375 on a new
computer.
Kim and her friend Stacey went
to the bookstore. Stacey spent
$8 on notebooks. Kim spent $5
on snacks and pencils.
At a beach in California, if a
person stands in the water, he
is
1
5
ft. below sea level. If the
person walks onto the beach,
he is
2
5
ft. above sea level.
Lesson 9:
© 2015 Great Minds. eureka-math.org
G6-M3-SAP-1.3.0-07.2015
Jayden has earned 3 bonus
points completing math extra
credit assignments, while
Shontelle has earned 32 bonus
points.
Last month, the stock market
3
dropped 5 points overall. So
4
far this month, the stock
1
4
market rose 3 points.
Brittany went to an office
supply store twice last week.
The first time, she made
2 copies that cost $0.20 each.
The second time, she did not
buy anything but found 2 dimes
in the parking lot.
Comparing Integers and Other Rational Numbers
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12
Lesson 10
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 10: Writing and Interpreting Inequality Statements
Involving Rational Numbers
Exit Ticket
Kendra collected data for her science project. She surveyed people asking them how many hours they sleep during a
typical night. The chart below shows how each person’s response compares to 8 hours (which is the answer she
expected most people to say).
Name
Number of Hours
(usually slept each night)
Frankie
8.5
Mr. Fields
Karla
Compared to 𝟖𝟖 Hours
0.5
7
−1.0
8
0
9.5
Louis
Tiffany
7
1.5
3
4
−
1
4
a.
Plot and label each of the numbers in the right-most column of the table above on the number line below.
b.
List the numbers from least to greatest.
c.
Using your answer from part (b) and inequality symbols, write one statement that shows the relationship
among all of the numbers.
Lesson 10:
© 2015 Great Minds. eureka-math.org
G6-M3-SAP-1.3.0-07.2015
Writing and Interpreting Inequality Statements Involving Rational
Numbers
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13
Lesson 10
NYS COMMON CORE MATHEMATICS CURRICULUM
6•3
Number Correct: ______
Rational Numbers: Inequality Statements—Round 1
Directions: Work in numerical order to answer Problems 1–33. Arrange each set of numbers in order according to the
inequality symbols.
1.
<
2.
3.
<
>
1 , −1 , 0
<
1 , −1 , 0
>
<
12.
13.
14.
4.
3 ½ , −3 ½ , 0
15.
5.
3 ½ , −3 ½ , 0
>
>
16.
6.
<
1 ,−½ ,½
17.
<
1 ,−½ ,½
18.
−3 , −4 , −5
19.
−13 , −14 , −15
20.
>
7.
8.
9.
>
<
<
>
<
<
>
10.
−13 , −14 , −15
21.
11.
−¼ , −1 , 0
22.
<
>
<
>
−¼ , −1 , 0
Lesson 10:
© 2015 Great Minds. eureka-math.org
G6-M3-SAP-1.3.0-07.2015
>
>
23.
>
>
>
7 , −6 , 6
<
17 , 4 , 16
25.
<
17 , 4 , 16
26.
>
0 , 12 , −11
27.
0 , 12 , −11
28.
<
1,¼ ,½
29.
−0.5 , − 1 , − 0.6
<
1,¼ ,½
30.
−0.5 , −1 , −0.6
>
− ½,½ ,0
31.
−8 , −9 , 8
<
−½ , ½ , 0
32.
−18 , −19 , −2
50 , −10 , 0
33.
−2 , − 3 , 1
>
<
<
>
>
>
<
<
<
>
<
<
24.
−50 , 10 , 0
25 , ¾ , − ¾
<
<
25 , ¾ , − ¾
>
>
2.2 , 2.3 , 2.4
>
>
1.2 , 1.3 , 1.4
>
>
0.2 , 0.3 , 0.4
>
<
<
<
>
<
>
<
<
<
>
<
−2 , − 3 , 1
Writing and Interpreting Inequality Statements Involving Rational
Numbers
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14
Lesson 10
NYS COMMON CORE MATHEMATICS CURRICULUM
6•3
Number Correct: ______
Improvement: ______
Rational Numbers: Inequality Statements—Round 2
Directions: Work in numerical order to answer Problems 1–33. Arrange each set of numbers in order according to the
inequality symbols.
1.
<
<
12.
2.
1/7 , −1/7 , 0
13.
3.
1/7 , −1/7 , 0
4.
>
>
23.
>
>
1¼ , 1 , 1½
24.
14.
11¼ , 11 , 11½
25.
3/7 , 2/7 , −1/7
15.
11¼ , 11 , 11½
26.
−82 , −93 , −104
5.
3/7 , 2/7 , −1/7
16.
0 , 0.2 , −0.1
27.
−82 , −93 , −104
6.
−4/5 , 1/5 , −1/5
17.
0 , 0.2 , −0.1
28.
0.5 , 1 , 0.6
7.
−4/5 , 1/5 , −1/5
18.
1 , 0.7, 1/10
29.
−0.5 , − 1 , −0.6
8.
−8/9 , 5/9, 1/9
19.
1 , 0.7, 1/10
30.
−0.5 , − 1 , −0.6
9.
−8/9 , 5/9, 1/9
20.
0 , −12 , −12½
31.
1 ,8,9
10.
−30 , −10 , −50
21.
0 , −12 , −12½
32.
11.
−30 , −10 , −50
22.
5 , −1 , 0
33.
>
<
>
>
<
<
>
>
<
>
>
<
>
>
<
<
>
>
<
>
−40 , −20 , −60
Lesson 10:
© 2015 Great Minds. eureka-math.org
G6-M3-SAP-1.3.0-07.2015
>
>
<
<
<
<
>
>
>
>
<
<
<
<
>
>
<
<
<
<
−5 , 1 , 0
1 , 1¾ , − 1¾
<
<
1 , 1¾ , − 1¾
>
>
<
<
>
>
>
>
<
<
<
<
<
<
−1 , −8 , −9
>
>
−2 , −3 , −5
>
>
2 ,3,5
Writing and Interpreting Inequality Statements Involving Rational
Numbers
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15
Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 11: Absolute Value—Magnitude and Distance
Exit Ticket
Jessie and his family drove up to a picnic area on a mountain. In the morning, they followed a trail that led to the
mountain summit, which was 2,000 feet above the picnic area. They then returned to the picnic area for lunch. After
lunch, they hiked on a trail that led to the mountain overlook, which was 3,500 feet below the picnic area.
a.
Locate and label the elevation of the mountain summit and mountain overlook on a vertical
number line. The picnic area represents zero. Write a rational number to represent each
location.
Picnic area:
Mountain summit:
0
Mountain overlook:
b.
Use absolute value to represent the distance on the number line of each location from the
picnic area.
Distance from the picnic area to the mountain summit:
Distance from the picnic area to the mountain overlook:
c.
What is the distance between the elevations of the summit and overlook? Use absolute value and your
number line from part (a) to explain your answer.
Lesson 11:
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Absolute Value—Magnitude and Distance
16
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Lesson 12
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 12: The Relationship Between Absolute Value and Order
Exit Ticket
1.
Bethany writes a set of rational numbers in increasing order. Her teacher asks her to write the absolute values of
these numbers in increasing order. When her teacher checks Bethany’s work, she is pleased to see that Bethany has
not changed the order of her numbers. Why is this?
2.
Mason was ordering the following rational numbers in math class: −3.3, −15, −8 .
a.
Order the numbers from least to greatest.
b.
List the order of their absolute values from least to greatest.
c.
Explain why the orderings in parts (a) and (b) are different.
Lesson 12:
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G6-M3-SAP-1.3.0-07.2015
8
9
The Relationship Between Absolute Value and Order
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Lesson 13
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 13: Statements of Order in the Real World
Exit Ticket
1.
Loni and Daryl call each other from different sides of Watertown. Their locations are shown on the number line
below using miles. Use absolute value to explain who is a farther distance (in miles) from Watertown. How much
closer is one than the other?
Loni
−10
2.
−8
−6
Daryl
Watertown
−4
−2
0
2
4
6
8
10
Claude recently read that no one has ever scuba dived more than 330 meters below sea level. Describe what this
means in terms of elevation using sea level as a reference point.
Lesson 13:
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Statements of Order in the Real World
18
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NYS COMMON CORE MATHEMATICS CURRICULUM
Mid-Module Assessment Task
Name
6•3
Date
1. The picture below is a flood gauge that is used to measure how far (in feet) a river’s water level is above
or below its normal level.
a.
Explain what the number 0 on the gauge represents, and explain what the numbers
above and below 0 represent.
1.5
1.0
0.5
0
−0.5
−1.0
−1.5
b.
Describe what the picture indicates about the river’s
current water level.
River Water
−2.0
−2.5
−3.0
−3.5
c.
What number represents the opposite of the water level shown in the picture, and where is it
located on the gauge? What would it mean if the river water was at that level?
d.
If heavy rain is in the forecast for the area for the next 24 hours, what reading might you expect to
see on this gauge tomorrow? Explain your reasoning.
Module 3:
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Rational Numbers
19
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Mid-Module Assessment Task
NYS COMMON CORE MATHEMATICS CURRICULUM
6•3
2. Isaac made a mistake in his checkbook. He wrote a check for $8.98 to rent a video game but mistakenly
recorded it in his checkbook as an $8.98 deposit.
a.
Represent each transaction with a rational number, and explain the difference between the
transactions.
b.
On the number line below, locate and label the points that represent the rational numbers listed in
part (a). Describe the relationship between these two numbers. Zero on the number line represents
Isaac’s balance before the mistake was made.
0
c.
Use absolute value to explain how a debit of $8.98 and a credit of $8.98 are similar.
Module 3:
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Rational Numbers
20
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Mid-Module Assessment Task
NYS COMMON CORE MATHEMATICS CURRICULUM
6•3
3. A local park’s programs committee is raising money by holding mountain bike races on a course through
the park. During each race, a computer tracks the competitors’ locations on the course using GPS
tracking. The table shows how far each competitor is from a checkpoint.
Number
Competitor Name
Distance to Checkpoint
223
Florence
0.1 miles before
231
240
249
a.
255
Mary
Rebecca
Lita
Nancy
2
5
miles past
0.5 miles before
2
1
2
10
miles past
miles before
The checkpoint is represented by 0 on the number line. Locate and label points on the number line
for the positions of each listed participant. Label the points using rational numbers.
0
Checkpoint
b.
Which of the competitors is closest to the checkpoint? Explain.
c.
Two competitors are the same distance from the checkpoint. Are they in the same location?
Explain.
d.
Who is closer to finishing the race, Nancy or Florence? Support your answer.
Module 3:
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Mid-Module Assessment Task
NYS COMMON CORE MATHEMATICS CURRICULUM
6•3
4. Andréa and Marta are testing three different coolers to see which keeps the coldest temperature. They
placed a bag of ice in each cooler, closed the coolers, and then measured the air temperature inside each
after 90 minutes. The temperatures are recorded in the table below:
Cooler
Temperature (ᵒC)
A
−2.91
B
5.7
C
−4.3
Marta wrote the following inequality statement about the temperatures:
−4.3 < −2.91 < 5.7.
Andréa claims that Marta made a mistake in her statement and that the inequality statement should be
written as
−2.91 < −4.3 < 5.7.
a.
Is either student correct? Explain.
b.
The students want to find a cooler that keeps the temperature inside the cooler more than
3 degrees below the freezing point of water (0ᵒC) after 90 minutes. Indicate which of the tested
coolers meets this goal, and explain why.
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Mid-Module Assessment Task
NYS COMMON CORE MATHEMATICS CURRICULUM
6•3
5. Mary manages a company that has been hired to flatten a plot of land. She took several elevation
samples from the land and recorded those elevations below:
Elevation Sample
Elevation
(ft. above sea level)
A
B
C
D
E
F
826.5
830.2
832.0
831.1
825.8
827.1
a.
The landowner wants the land flat and at the same level as the road that passes in front of it. The
road’s elevation is 830 feet above sea level. Describe in words how elevation samples B, C, and E
compare to the elevation of the road.
b.
The table below shows how some other elevation samples compare to the level of the road:
Elevation Sample
Elevation
(ft. from the road)
G
H
I
J
K
L
3.1
−0.5
2.2
1.3
−4.5
−0.9
Write the values in the table in order from least to greatest.
_________< _________ < _________ < _________ < _________ < _________
c.
Indicate which of the values from the table in part (b) is farthest from the elevation of the road.
Use absolute value to explain your answer.
Module 3:
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Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 14: Ordered Pairs
Exit Ticket
1.
On the map below, the fire department and the hospital have one matching coordinate. Determine the proper
order of the ordered pairs in the map, and write the correct ordered pairs for the locations of the fire department
and hospital. Indicate which of their coordinates are the same.
2.
On the map above, locate and label the locations of each description below:
a.
The local bank has the same first coordinate as the fire department, but its second coordinate is half of the fire
department’s second coordinate. What ordered pair describes the location of the bank? Locate and label the
bank on the map using point 𝐵𝐵.
b.
The Village Police Department has the same second coordinate as the bank, but its first coordinate is −2.
What ordered pair describes the location of the Village Police Department? Locate and label the Village Police
Department on the map using point 𝑃𝑃.
Lesson 14:
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Ordered Pairs
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Lesson 15
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 15: Locating Ordered Pairs on the Coordinate Plane
Exit Ticket
1.
2.
Label the second quadrant on the coordinate plane, and
then answer the following questions:
a.
Write the coordinates of one point that lies in the
second quadrant of the coordinate plane.
b.
What must be true about the coordinates of any
point that lies in the second quadrant?
Label the third quadrant on the coordinate plane, and then
answer the following questions:
a.
Write the coordinates of one point that lies in the third quadrant of the coordinate plane.
b.
What must be true about the coordinates of any point that lies in the third quadrant?
3.
An ordered pair has coordinates that have the same sign. In which quadrant(s) could the point lie? Explain.
4.
Another ordered pair has coordinates that are opposites. In which quadrant(s) could the point lie? Explain.
Lesson 15:
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Locating Ordered Pairs on the Coordinate Plane
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25
Lesson 16
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 16: Symmetry in the Coordinate Plane
Exit Ticket
1.
How are the ordered pairs (4, 9) and (4, −9) similar, and how are they different? Are the two points related by a
reflection over an axis in the coordinate plane? If so, indicate which axis is the line of symmetry between the points.
If they are not related by a reflection over an axis in the coordinate plane, explain how you know.
2.
Given the point (−5, 2), write the coordinates of a point that is related by a reflection over the 𝑥𝑥- or 𝑦𝑦-axis. Specify
which axis is the line of symmetry.
Lesson 16:
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Symmetry in the Coordinate Plane
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Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 17: Drawing the Coordinate Plane and Points on the Plane
Exit Ticket
Determine an appropriate scale for the set of points given below. Draw and label the coordinate plane, and then locate
and label the set of points.
{(10, 0.2), (−25, 0.8), (0, −0.4), (20, 1), (−5, −0.8)}
Lesson 17:
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Drawing the Coordinate Plane and Points on the Plane
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27
Lesson 18
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 18: Distance on the Coordinate Plane
Exit Ticket
Determine whether each given pair of end points lies on the same horizontal or vertical line. If so, find the length of the
line segment that joins the pair of points. If not, explain how you know the points are not on the same horizontal or
vertical line.
a.
(0, −2) and (0, 9)
b.
(11, 4) and (2, 11)
c.
(3, −8) and (3, −1)
d.
(−4, −4) and (5, −4)
Lesson 18:
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Distance on the Coordinate Plane
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Lesson 19
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
Lesson 19: Problem Solving and the Coordinate Plane
Exit Ticket
1.
The coordinates of one end point of a line segment are (−2, −7). The line segment is 12 units long. Give three
possible coordinates of the line segment’s other end point.
2.
Graph a rectangle with an area of 12 units2 such that its vertices lie in at least two of the four quadrants in the
coordinate plane. State the lengths of each of the sides, and use absolute value to show how you determined the
lengths of the sides.
𝒚𝒚
𝒙𝒙
Lesson 19:
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Problem Solving and the Coordinate Plane
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End-of-Module Assessment Task
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•3
Date
1. Mr. Kindle invested some money in the stock market. He tracks his gains and losses using a computer
program. Mr. Kindle receives a daily email that updates him on all his transactions from the previous day.
This morning, his email read as follows:
Good morning, Mr. Kindle,
a.
Yesterday’s investment activity included a loss of $800, a gain of $960, and another gain of
$230. Log in now to see your current balance.
Write an integer to represent each gain and loss.
Description
Integer Representation
Loss of $800
Gain of $960
Gain of $230
b.
Mr. Kindle noticed that an error had been made on his account. The “loss of $800” should have
been a “gain of $800.” Locate and label both points that represent “a loss of $800” and “a gain of
$800” on the number line below. Describe the relationship of these two numbers when zero
represents no change (gain or loss).
0
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NYS COMMON CORE MATHEMATICS CURRICULUM
c.
End-of-Module Assessment Task
6•3
Mr. Kindle wanted to correct the error, so he entered −(−$800) into the program. He made a note
that read, “The opposite of the opposite of $800 is $800.” Is his reasoning correct? Explain.
2. At 6:00 a.m., Buffalo, NY, had a temperature of 10℉. At noon, the temperature was −10℉, and at
midnight, it was −20℉.
Temperature in degrees Fahrenheit
a.
Write a statement comparing −10℉ and −20℉.
b.
Write an inequality statement that shows the relationship between the three recorded
temperatures. Which temperature is the warmest?
Module 3:
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
6•3
c.
Explain how to use absolute value to find the number of degrees below zero the temperature was at
noon.
d.
In Peekskill, NY, the temperature at 6:00 a.m. was −12℉. At noon, the temperature was the exact
opposite of Buffalo’s temperature at 6:00 a.m. At midnight, a meteorologist recorded the
temperature as −6℉ in Peekskill. He concluded that “For temperatures below zero, as the
temperature increases, the absolute value of the temperature decreases.” Is his conclusion valid?
Explain and use a vertical number line to support your answer.
3. Choose an integer between 0 and −5 on a number line, and label the point 𝑃𝑃. Locate and label each of
the following points and their values on the number line.
−10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0
a.
b.
c.
d.
1
2
3
4
5
6
7
8
9
10
Label point 𝐴𝐴: the opposite of point 𝑃𝑃.
Label point 𝐵𝐵: a number less than point 𝑃𝑃.
Label point 𝐶𝐶: a number greater than point 𝑃𝑃.
Label point 𝐷𝐷: a number halfway between point 𝑃𝑃 and the integer to the right of point 𝑃𝑃.
Module 3:
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
6•3
4. Julia is learning about elevation in math class. She decided to research some facts about New York State
to better understand the concept. Here are some facts that she found.






a.
Mount Marcy is the highest point in New York State. It is 5,343 feet above sea level.
Lake Erie is 210 feet below sea level.
The elevation of Niagara Falls, NY, is 614 feet above sea level.
The lobby of the Empire State Building is 50 feet above sea level.
New York State borders the Atlantic Coast, which is at sea level.
The lowest point of Cayuga Lake is 435 feet below sea level.
Write an integer that represents each location in relationship to sea level.
Mount Marcy
Lake Erie
Niagara Falls, NY
Empire State Building
Atlantic Coast
Cayuga Lake
b.
Explain what negative and positive numbers tell Julia about elevation.
Module 3:
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NYS COMMON CORE MATHEMATICS CURRICULUM
c.
6•3
Order the elevations from least to greatest, and then state their absolute values. Use the chart
below to record your work.
Elevations
d.
End-of-Module Assessment Task
Absolute Values of Elevations
Circle the row in the table that represents sea level. Describe how the order of the elevations below
sea level compares to the order of their absolute values. Describe how the order of the elevations
above sea level compares to the order of their absolute values.
Module 3:
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
6•3
5. For centuries, a mysterious sea serpent has been rumored to live at the bottom of Mysterious Lake. A
team of historians used a computer program to plot the last five positions of the sightings.
E
a.
b.
1
Locate and label the locations of the last four sightings: 𝐴𝐴 �−9 2 , 0�, 𝐵𝐵(−3, −4.75), 𝐶𝐶(9, 2),
and 𝐷𝐷(8, −2.5).
Over time, most of the sightings occurred in Quadrant III. Write the coordinates of a point that lies
in Quadrant III.
1
c.
What is the distance between point 𝐴𝐴 and the point �9 2 , 0�? Show your work to support your
answer.
d.
What are the coordinates of point 𝐸𝐸 on the coordinate plane?
e.
Point 𝐹𝐹 is related to point 𝐸𝐸. Its 𝑥𝑥-coordinate is the same as point 𝐸𝐸’s, but its 𝑦𝑦-coordinate is the
opposite of point 𝐸𝐸’s. Locate and label point 𝐹𝐹. What are the coordinates? How far apart are points
𝐸𝐸 and 𝐹𝐹? Explain how you arrived at your answer.
Module 3:
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Rational Numbers
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